fstsne {TDAkit}

t-distributed Stochastic Neighbor Embedding

Description

Given N functional summaries \Lambda_1 (t), \Lambda_2 (t), \ldots, \Lambda_N (t), t-SNE mimicks the pattern of probability distributions over pairs of Banach-valued objects on low-dimensional target embedding space by minimizing Kullback-Leibler divergence.

Usage

fstsne(fslist, ndim = 2, ...)

Arguments

fslist

a length-N list of functional summaries of persistent diagrams.

ndim

an integer-valued target dimension.

...

extra parameters for Rtsne algorithm, such as perplexity, momentum, and others.

Value

a named list containing

embed

an (N\times ndim) matrix whose rows are embedded observations.

stress

discrepancy between embedded and original distances as a measure of error.

See Also

Rtsne

Examples

# ---------------------------------------------------------------------------
#     Multidimensional Scaling for Multiple Landscapes and Silhouettes
#
# We will compare dim=0 with top-5 landscape and silhouette functions with 
# - Class 1 : 'iris' dataset with noise
# - Class 2 : samples from 'gen2holes()'
# - Class 3 : samples from 'gen2circles()'
# ---------------------------------------------------------------------------
## Generate Data and Diagram from VR Filtration
ndata     = 10
list_rips = list()
for (i in 1:ndata){
  dat1 = as.matrix(iris[,1:4]) + matrix(rnorm(150*4), ncol=4)
  dat2 = gen2holes(n=100, sd=1)$data
  dat3 = gen2circles(n=100, sd=1)$data
  
  list_rips[[i]] = diagRips(dat1, maxdim=1)
  list_rips[[i+ndata]] = diagRips(dat2, maxdim=1)
  list_rips[[i+(2*ndata)]] = diagRips(dat3, maxdim=1)
}

## Compute Landscape and Silhouettes of Dimension 0
list_land = list()
list_sils = list()
for (i in 1:(3*ndata)){
  list_land[[i]] = diag2landscape(list_rips[[i]], dimension=0)
  list_sils[[i]] = diag2silhouette(list_rips[[i]], dimension=0)
}
list_lab = rep(c(1,2,3), each=ndata)

## Run t-SNE and Classical/Metric MDS
land_cmds = fsmds(list_land, method="classical")
land_mmds = fsmds(list_land, method="metric")
land_tsne = fstsne(list_land, perplexity=5)$embed
sils_cmds = fsmds(list_sils, method="classical")
sils_mmds = fsmds(list_sils, method="metric")
sils_tsne = fstsne(list_land, perplexity=5)$embed

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,3))
plot(land_cmds, pch=19, col=list_lab, main="Landscape+CMDS")
plot(land_mmds, pch=19, col=list_lab, main="Landscape+MMDS")
plot(land_tsne, pch=19, col=list_lab, main="Landscape+tSNE")
plot(sils_cmds, pch=19, col=list_lab, main="Silhouette+CMDS")
plot(sils_mmds, pch=19, col=list_lab, main="Silhouette+MMDS")
plot(sils_tsne, pch=19, col=list_lab, main="Silhouette+tSNE")
par(opar)